2 Answers
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The general rule of thumb for shabbat is that any action required for security related reasons (operation of jeeps, radio check ins, patrols, etc) during the week should be performed on shabbat as well.

I.E. you shouldn't be lowering the level of security because it's shabbat.

There are standing orders at all levels in the IDF which prevent the giving of orders that violate shabbat in non life saving matters. Having said that, if your commander isn't knowledgeable in hilchot Shabbat, you may have issues. These should of course be preferably anticipated before shabbat and discussed in a non confrontational manner.

This is based on what I learnt from my Rabbanim at Yeshivat Har Etzion (Rav B Gigi/Rav Y Rimon) during a pre-army series of shiurim.

Practically speaking, Basic Training isn't purely training. It involves protecting the base from real threats and while you're unlikely to invade Ramallah there will be plenty of guard duty in all sorts of places which require protection.

I imagine that it would be next to impossible to keep Shabbat in any army other than the IDF, simply because much of Basic Training can't be justified as pikuach nefesh on shabbat.

Of course, anyone intending to keep Shabbat and other halachot in the army should find a Rabbi familiar with the halachic challenges of being in the IDF and talk with them beforehand. I'm sure any Hesder Yeshiva or Mechina would be happy to help.

All IDF units have a Rabbi who can provide a well written pocket sized book (in hebrew only) with lots of tips, halachot and numbers to call if you have a question.